318 Mr. G. A. Campbell on Loaded 



and (12) may be written 





(6+ 



«')ci,-(^. + f/) r . . . (17) 



where the second and third factors are, respectively, the 

 effective attenuation and the phase lag due to the line. As 

 b can be negative, reflexion may augment the receiving- 

 current, but in general the effect is a loss which may be 

 comparable with the attenuation loss. Thus for #/J s =10, 

 6 = I'll, and the range of "easy commercial'" telephonic 

 transmission, which requires an effective attenuation co- 

 efficient o£ 3*2 with present instruments, would be reduced 

 1*1 1/3*2, or 35 per cent. 



By Diagram I. (PL V.) the transformer efficiency in equation 

 (13«) is a maximum and completely offsets the reflexion loss 

 when J 2 /Ji= k/J s | — >'• It follows that, by introducing trans- 

 formers into a line at every point of non-uniformity due to 

 apparatus or a change in line construction, reflexion losses 

 may be entirely eliminated and the effective attenuation made 

 as small as or smaller than the real line attenuation. 



The effect of loading a line uniformly is shown by Diagram II. 

 (PL A 7 .), which gives the attenuation coefficient for lines having 

 R = 2, = 1, and different values of L. Also the velocity, 

 for with these values of the constants the velocity and 

 attenuation coefficient are numerically equaL With no in- 

 ductance the attenuation curve is a parabola. Any increase 

 in inductance reduces the attenuation and makes it more 

 nearly uniform, and by a sufficient increase in the inductance 

 the attenuation can be reduced to any desired value, but for 

 this it is essential that the leakage be null. 



The effect of leakage is added in Diagram III. (PLY.), which 

 is plotted for K=l, L==l, C = l + /u,, 8 = 1 — /^ but gives the 

 attenuation coefficient and velocity curves for any uniform 

 line by a change in scales only. 



II. 



An infinite loaded line will be considered first in order to 

 treat propagation and terminal conditions separately. We 

 might follow in detail the repeated division of the wave by 

 reflexion at loads and the interference of the resulling wave- 

 lets which mutually annul each other, with the exception of 

 a group suffering reflexion and transmission in a certain ratio 

 which gives rise to a wave of small attenuation and negli- 

 gible distortion, although the individual wavelets may be 

 enormously attenuated and distorted by the length of their 



